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Frequency-Domain Adaptive Filters

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Frequency-Domain Adaptive Filters Powered By Docstoc
       Adaptive Filters

                Wu, Yihong
                EE 491D
 n   Advantages of FDAF
 n   Block-Adaptive Filters (BAF)
 n   Convergence Properties
 n   Choice of Block Size
 n   Methods
 n   Computational Complexity
Advantages of FDAF
  n   Providing a possible solution to the
      computational complexity problem

  n   Attaining a more uniform convergence
      rate by exploiting the orthogonality
      properties of DFT
Block-Adaptive Filters (BAF)
     n   BAF Diagram

     n   BLMS Equations

     n   Convergence behavior
BAF Diagram

 Figure 1: Block-adaptive filter
BLMS Equations
 § From the conventional LMS, we could get the
   following equations for BLMS
BLMS Equations(cont.)
   n       Tap-weight updated once after collection of every
           block of data samples

       n L is the block length
       n     is the effective step-size parameter
       nError is the difference between the output
       and the desired signal
BLMS Equations(cont.)
   n   If written in matrices format:
     Convergence Properties
n   Average time constant equation:

n   If    is the same for both conventional LMS and BLMS, they
    would have the same average time constant.

n   For zero-order formula, the      will be small while comparing
    to 1/    .

n   For fast adaptation,        is small and L is large, so   will be
    so large that the higher order effects would cause instability
    problems. BLMS could overcome the problem.
Choice of Block Size
 n   L = M: optimal choice for computational

 n   L < M: offers the advantage of reduced
     processing delay

 n   L > M: gives rise to redundant operations in
     the adaptive process

 n   Overall, L = M is the best choice
n   Overlap-Save Sectioning

n   Overlap-Add Sectioning

n   Circular Convolution
    Overlap-Save Sectioning
§   Linear convolution between a finite-length sequence
    [w(n)]and an infinite-length sequence [x(n)].

§   Zero-padding w(n) from N-point to 2N-point

§   FFT both x(n) and w(n) to get Y(k)

§   First N point data would be ignored

§   Only looking for the last N point data
Overlap-Save Sectioning

  Figure 2: Overlap-Save Sectioning.
Overlap-Save Sectioning

   Figure 3: Overlap-Save FDAF
Overlap-Save Sectioning
    n   FDAF Algorithm Based on
        Overlap-Save Sectioning
Overlap-Add Sectioning
      n   Input signal is different

      nOutput y(k)
      nError E(k)
Overlap-Add Sectioning

   Figure 4: Overlap-Add FDAF.
     Overlap-Add Sectioning
n   FDAF Algorithm Based on Overlap-Add
Circular Convolution
    n   Reducing complexity
    n   Causing additional degradation
    n   Constraint matrices have been
    n   Rank of F is M = N
        u Data is not overlapping any more
        u Error is always linear between Y(K)
          and D(K)
Circular Convolution

 Figure 5: Circular-Convolution FDAF.
    Circular Convolution
n   FDAF Algorithm Based on Circular
Computational Complexity
     n   Equation

     nDepending on the filter size
     nGreatest: Linear convolution

     nSmallest: Circular convulution
Computational Complexity

      Table 1: FDAF computational
        complexity ratios
  n   Advantages of FDAF
  n   Computational Complexity
  n   Some methods
  n   Potential to be developed in
      the future
Thank you very much!

 Have a nice Summer!

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